MAYBE

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict Trs:
  { g(x, y) -> x
  , g(x, y) -> y
  , f(x, y, s(z)) -> s(f(0(), 1(), z))
  , f(0(), 1(), x) -> f(s(x), x, x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

We add following weak dependency pairs:

Strict DPs:
  { g^#(x, y) -> c_1()
  , g^#(x, y) -> c_2()
  , f^#(x, y, s(z)) -> c_3(f^#(0(), 1(), z))
  , f^#(0(), 1(), x) -> c_4(f^#(s(x), x, x)) }

and mark the set of starting terms.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { g^#(x, y) -> c_1()
  , g^#(x, y) -> c_2()
  , f^#(x, y, s(z)) -> c_3(f^#(0(), 1(), z))
  , f^#(0(), 1(), x) -> c_4(f^#(s(x), x, x)) }
Strict Trs:
  { g(x, y) -> x
  , g(x, y) -> y
  , f(x, y, s(z)) -> s(f(0(), 1(), z))
  , f(0(), 1(), x) -> f(s(x), x, x) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

No rule is usable, rules are removed from the input problem.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { g^#(x, y) -> c_1()
  , g^#(x, y) -> c_2()
  , f^#(x, y, s(z)) -> c_3(f^#(0(), 1(), z))
  , f^#(0(), 1(), x) -> c_4(f^#(s(x), x, x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The weightgap principle applies (using the following constant
growth matrix-interpretation)

The following argument positions are usable:
  Uargs(c_3) = {1}, Uargs(c_4) = {1}

TcT has computed following constructor-restricted matrix
interpretation.

                [0] = [1]         
                                  
                [1] = [1]         
                                  
            [s](x1) = [1] x1 + [1]
                                  
      [g^#](x1, x2) = [1]         
                                  
              [c_1] = [0]         
                                  
              [c_2] = [0]         
                                  
  [f^#](x1, x2, x3) = [1] x3 + [2]
                                  
          [c_3](x1) = [1] x1 + [2]
                                  
          [c_4](x1) = [1] x1 + [2]

This order satisfies following ordering constraints:


Further, it can be verified that all rules not oriented are covered by the weightgap condition.

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(x, y, s(z)) -> c_3(f^#(0(), 1(), z))
  , f^#(0(), 1(), x) -> c_4(f^#(s(x), x, x)) }
Weak DPs:
  { g^#(x, y) -> c_1()
  , g^#(x, y) -> c_2() }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The following weak DPs constitute a sub-graph of the DG that is
closed under successors. The DPs are removed.

{ g^#(x, y) -> c_1()
, g^#(x, y) -> c_2() }

We are left with following problem, upon which TcT provides the
certificate MAYBE.

Strict DPs:
  { f^#(x, y, s(z)) -> c_3(f^#(0(), 1(), z))
  , f^#(0(), 1(), x) -> c_4(f^#(s(x), x, x)) }
Obligation:
  innermost runtime complexity
Answer:
  MAYBE

The input cannot be shown compatible

Arrrr..